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Paper Citation Record · LEDGER

Some Mathematical Problems Behind Lattice-Based Cryptography

As of 13 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2506.23438.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.23438 v1

Coverage vector

measured 50 of 50 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:50:16.650375Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

50 of 50 outbound references displayed

  • verified exact2
  • verified fuzzy35
  • unresolved13
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 634ed928-349e-40fa-8f74-605a1217fbb8 · outbound

This paper cites Aggarwal, Y.

Some Mathematical Problems Behind Lattice-Based Cryptography Aggarwal, Y

Reference 1

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raw_fallback, observed 2026-08-06T21:50:26.442117Z

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source=pdf_text observed=2026-08-06T21:50:11.422940Z digest=sha256:f9d5e9cb202e4cfd5ab1c47b222238aee1b254e360bcee9f89f644ef7c813e10

Observation 844cbf03-ee1b-42f2-b80b-063881f3c2ee · outbound

This paper cites Ajtai, The shortest vector problem in L2 is NP-hard for randomized reductions.

Some Mathematical Problems Behind Lattice-Based Cryptography Ajtai, The shortest vector problem in L2 is NP-hard for randomized reductions

Reference 2

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source=pdf_text observed=2026-08-06T21:50:11.497464Z digest=sha256:225ef7183ae16a91bc6e17017ffe4d838e635003863cb07def2d410867779b68

Observation 53f4b365-7202-4ff4-a7f4-567f29e87f48 · outbound

This paper cites Ajtai, Generating hard instances of lattice problems.

Some Mathematical Problems Behind Lattice-Based Cryptography Ajtai, Generating hard instances of lattice problems

Reference 3

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source=pdf_text observed=2026-08-06T21:50:11.587316Z digest=sha256:79c9cd23e277c8a17627cf1f9683d8af4daf40d46ca7168e1ccad8909b388403

Observation 4d5d20ea-ef68-4009-b3bb-f4c336d9daa2 · outbound

This paper cites Ajtai and C.

Some Mathematical Problems Behind Lattice-Based Cryptography Ajtai and C

Reference 4

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raw_fallback, observed 2026-08-06T21:50:25.827202Z

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source=pdf_text observed=2026-08-06T21:50:11.675440Z digest=sha256:772080fad175b0be1fddd8dd693770fc452e55b0b2465c53c5bb58123cdaad4c

Observation ef568a0d-f1a4-41e1-9c2b-5e69e02f6529 · outbound

This paper cites A Survey on Post-Quantum Cryptography: State-of-the-Art and Challenges.

Some Mathematical Problems Behind Lattice-Based Cryptography A Survey on Post-Quantum Cryptography: State-of-the-Art and Challenges

Reference 5

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local_arxiv, observed 2026-08-06T21:50:17.224211Z

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source=pdf_text observed=2026-08-06T21:50:11.771763Z digest=sha256:4e70fe139399da3d77249b67f8f890d16aa0688692d4c2b9cee8692fb37ccc9b

Observation 3174028b-a7a8-4754-a05e-c459f3d7a4e5 · outbound

This paper cites Babai, On Lov´ asz’ lattice reduction and the nearest lattice point problem.

Some Mathematical Problems Behind Lattice-Based Cryptography Babai, On Lov´ asz’ lattice reduction and the nearest lattice point problem

Reference 6

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raw_fallback, observed 2026-08-06T21:50:25.592389Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:11.844329Z digest=sha256:26ecd6ce5ed62b312b601a1a0c89d10dda86a56146ac0d7f61be9fbc06e254aa

Observation 82e354c5-bd27-4052-b15a-14a0ee7616d1 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 7

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source=pdf_text observed=2026-08-06T21:50:11.957061Z digest=sha256:3d33c43881500d1cbef3e98100595b2747b6d40061293eb98c2471fd665a712b

Observation 258608df-42bd-4a34-bc0e-1c420613e0f1 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 8

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source=pdf_text observed=2026-08-06T21:50:12.028184Z digest=sha256:de7895e9c45c23ae8f862e936899178dad58c8743ce2ccf9dc497723d9b06b90

Observation b9e484bd-2533-42cf-bdbd-0d935d978d48 · outbound

This paper cites Deutsch and R.

Some Mathematical Problems Behind Lattice-Based Cryptography Deutsch and R

Reference 9

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source=pdf_text observed=2026-08-06T21:50:12.262359Z digest=sha256:955332a15ef518ea8699999d85fcea7ee0ea741f92c6d70e1da2054029ad4b0d

Observation d6d20e01-7f1b-4e8a-a315-250f7b5efa43 · outbound

This paper cites Diffie and M.

Some Mathematical Problems Behind Lattice-Based Cryptography Diffie and M

Reference 10

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source=pdf_text observed=2026-08-06T21:50:12.389198Z digest=sha256:9c34752e2830f335671110732bf0e99c7c123d03dc9cda51015dcd264ad26d1a

Observation 0ff581db-0eb2-45d9-a5eb-265ec8afa12f · outbound

This paper cites Dinur, G.

Some Mathematical Problems Behind Lattice-Based Cryptography Dinur, G

Reference 11

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source=pdf_text observed=2026-08-06T21:50:12.504426Z digest=sha256:cfb42004957795585acf06e3237f96182ab42115ca7d92fcc29c3b052fbaa573

Observation 66a7079b-3f96-4d89-869d-ed9d14316e15 · outbound

This paper cites ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms.

Some Mathematical Problems Behind Lattice-Based Cryptography ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms

Reference 12

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source=pdf_text observed=2026-08-06T21:50:12.593833Z digest=sha256:f704c3a446adf97e50e56ae4190a43fb108b39c8039c72f76eb707623ce840e9

Observation db368c53-b5f3-4c89-a0a1-9dc716b7c28f · outbound

This paper cites Gentry, Fully homomorphic encryption using ideal lattices.

Some Mathematical Problems Behind Lattice-Based Cryptography Gentry, Fully homomorphic encryption using ideal lattices

Reference 13

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source=pdf_text observed=2026-08-06T21:50:12.659849Z digest=sha256:53deb651f7e0f4a183b71a5f60afb7d3f8ec3d0816171d0f1b42a79e4b599716

Observation a364beec-bf0c-4e90-be68-f511d6171cb1 · outbound

This paper cites Goldreich, S.

Some Mathematical Problems Behind Lattice-Based Cryptography Goldreich, S

Reference 14

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raw_fallback, observed 2026-08-06T21:50:23.812170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:12.747070Z digest=sha256:d4e61880a470b168cba93513b876c967feba9b1ab5316c352defc858e46d6daa

Observation 74fbaf08-8d4a-4883-a586-9fe0dd4d28e3 · outbound

This paper cites Goldreich, D.

Some Mathematical Problems Behind Lattice-Based Cryptography Goldreich, D

Reference 15

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verified fuzzy
raw_fallback, observed 2026-08-06T21:50:23.683136Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:12.859503Z digest=sha256:47d677093895abb60a8a2ee33026152df5dc7143991308e457cd464b386852ad

Observation a33e3996-c776-49ee-9592-b6a5677a13d1 · outbound

This paper cites Goldwasser, Mathematical foundations of modern cryptography: computational complexity perspective.

Some Mathematical Problems Behind Lattice-Based Cryptography Goldwasser, Mathematical foundations of modern cryptography: computational complexity perspective

Reference 16

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raw_fallback, observed 2026-08-06T21:50:23.530588Z

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source=pdf_text observed=2026-08-06T21:50:12.973869Z digest=sha256:11eb9ae0e8e9c4f23e7281d4a7e513323f181dbaf3d22d819d3584768ae07182

Observation 9e63a1ba-2ab9-47fd-bccf-05d3c7f5100d · outbound

This paper cites Hoffstein, J.

Some Mathematical Problems Behind Lattice-Based Cryptography Hoffstein, J

Reference 17

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raw_fallback, observed 2026-08-06T21:50:23.294566Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:13.047616Z digest=sha256:009ed39845d3141285bde1dda30c8b14250de5b8345be3ad9af4cf844e0f14aa

Observation 71264e16-4eac-4d6d-a0e6-480f6897069a · outbound

This paper cites Hoffstein, J.

Some Mathematical Problems Behind Lattice-Based Cryptography Hoffstein, J

Reference 18

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raw_fallback, observed 2026-08-06T21:50:23.145107Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:13.140585Z digest=sha256:197a2154cdba1128553772f395c47aa9c3f0f8973071cef8f84ced9aafef7e4d

Observation 125f2e3a-8b27-4ec6-97d5-7dd006059e76 · outbound

This paper cites Kannan and L.

Some Mathematical Problems Behind Lattice-Based Cryptography Kannan and L

Reference 19

Resolution
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raw_fallback, observed 2026-08-06T21:50:22.938833Z

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source=pdf_text observed=2026-08-06T21:50:13.233402Z digest=sha256:9293a384a10e8bffdea6e0f7f23f0a433ab7e130d72e99eaf23bb1291832a502

Observation fcc4c698-1127-4367-b9cf-9ae565e3bc02 · outbound

This paper cites Khot, Hardness of approximating the shortest vector problem in lattices.

Some Mathematical Problems Behind Lattice-Based Cryptography Khot, Hardness of approximating the shortest vector problem in lattices

Reference 20

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raw_fallback, observed 2026-08-06T21:50:22.738548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:13.333483Z digest=sha256:ea9a7362b6b92937a112d389134e16c40eb25556260cdd74abaee5d19bd96ede

Observation 97c4245d-f3bc-4767-badb-d7b207fad958 · outbound

This paper cites Klartag, Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid, arXiv:2504.05042.

Some Mathematical Problems Behind Lattice-Based Cryptography Klartag, Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid, arXiv:2504.05042

Reference 21

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no resolver link, observed 2026-08-06T21:50:13.426470Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T21:50:13.426470Z digest=sha256:1183c4ed0a4b63a6eb9d75cb3506990c1bcaffb087bf6005810d95920eb521fd

Observation 9665702a-8f67-483b-be00-719f072748eb · outbound

This paper cites Koblitz, Elliptic curve cryptosystems.

Some Mathematical Problems Behind Lattice-Based Cryptography Koblitz, Elliptic curve cryptosystems

Reference 22

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source=pdf_text observed=2026-08-06T21:50:13.545898Z digest=sha256:90241c3864a74cbdff2450d8f9a9d738af3377a051743002865b0da5381dc8a5

Observation e3591639-09b5-45d9-ae01-540303a51cc1 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 23

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source=pdf_text observed=2026-08-06T21:50:13.653195Z digest=sha256:9272f6c96fb2fd579ef6f831a90a4056a427e5974fa07f6b5d23b53a65041e54

Observation 68ddf398-6ab3-4838-94f1-45105cc9e851 · outbound

This paper cites of Math.(2) 185 (2017), no.

Some Mathematical Problems Behind Lattice-Based Cryptography of Math.(2) 185 (2017), no

Reference 24

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raw_fallback, observed 2026-08-06T21:50:25.053312Z

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source=pdf_text observed=2026-08-06T21:50:12.141912Z digest=sha256:2ada20254326cf7799934b8b7626a20d4601fe36d175fe308d375e3a79f77ed1

Observation 429289dd-8449-4aa5-89d0-f51948871e3a · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 25

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source=pdf_text observed=2026-08-06T21:50:13.777997Z digest=sha256:a72739915a2ed188e587d512cc26eff887de00d300c9230482a3a5467ec09c8c

Observation 4b35a03e-4968-4948-8415-1f2d3091c838 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 26

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raw_fallback, observed 2026-08-06T21:50:21.841385Z

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source=pdf_text observed=2026-08-06T21:50:13.890274Z digest=sha256:a9e2a5c46c252309d1b1a71e539991cc80e57a6902ff55d49c1e3ee9741062f6

Observation 838fef99-e952-46b1-9cb2-52c667a4ffd7 · outbound

This paper cites Micciancio, Almost perfect lattices, the covering radius problem, and applications to Ajtai’s connection factor, SIAM J.

Some Mathematical Problems Behind Lattice-Based Cryptography Micciancio, Almost perfect lattices, the covering radius problem, and applications to Ajtai’s connection factor, SIAM J

Reference 27

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raw_fallback, observed 2026-08-06T21:50:21.603455Z

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source=pdf_text observed=2026-08-06T21:50:13.988669Z digest=sha256:a2c4df06271e04ed37b2fdc1d829890275378c6597c9e901cd03ea559caa763e

Observation d611a91c-30ce-4909-8083-b7a841d8729a · outbound

This paper cites Micciancio and S.

Some Mathematical Problems Behind Lattice-Based Cryptography Micciancio and S

Reference 28

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raw_fallback, observed 2026-08-06T21:50:21.400298Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:14.111414Z digest=sha256:fff55ae5db34a0bdcdd686022f480373a461764cadd71b76ac427e5fb6da2611

Observation 99c5411f-348a-46fb-8b9b-00ea8d45d685 · outbound

This paper cites Micciancio and O.

Some Mathematical Problems Behind Lattice-Based Cryptography Micciancio and O

Reference 29

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raw_fallback, observed 2026-08-06T21:50:21.189028Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:14.124411Z digest=sha256:94cefd68843a115d4a3721b54494f8111902c30e0b2304c4d202b3824f98c90e

Observation dcec256c-6527-4f46-a6ce-1fd7f7cb6ad3 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 30

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raw_fallback, observed 2026-08-06T21:50:20.940275Z

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source=pdf_text observed=2026-08-06T21:50:14.128897Z digest=sha256:11eb425eec97e1a99f383c8c882daa330d07ff8588aa91f47f69dcb7d2b95c3b

Observation 9441d6f0-013f-4336-84f7-604b721fadc8 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 31

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raw_fallback, observed 2026-08-06T21:50:20.719207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:14.220864Z digest=sha256:53667e7af2d5b49ad0c1d1a324ab127947c00984d63ee161378a935fe8d1b027

Observation c8aef107-44b1-41de-b857-668606e130c6 · outbound

This paper cites Ordentlich, O.

Some Mathematical Problems Behind Lattice-Based Cryptography Ordentlich, O

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:20.547051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:14.420350Z digest=sha256:11f89626c4dde1ed20d0f70fe1844c854c7008aa2aed36d9e42f0437dc0c0405

Observation 9509a123-125a-46b7-953f-034038582e6f · outbound

This paper cites Peikert, A Decade of Lattice Cryptography, Found.

Some Mathematical Problems Behind Lattice-Based Cryptography Peikert, A Decade of Lattice Cryptography, Found

Reference 33

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raw_fallback, observed 2026-08-06T21:50:20.360092Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:14.588619Z digest=sha256:4ff98d3a573aa5e38a7198933075cf5178e9cb9cce1d31dd179bcaecb3fe7ce9

Observation 9f5c365d-02ae-4fc0-ba4b-19244ebcfa42 · outbound

This paper cites Proos and C.

Some Mathematical Problems Behind Lattice-Based Cryptography Proos and C

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:20.198097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:14.750197Z digest=sha256:1bd8d76fa0c26ca195dc5a7c8a3f22ed122ed933cb23c598af4c5dcd6f79cdfe

Observation 89c25852-d4d7-48fc-a8ac-2832659a5397 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 35

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unresolved
raw_fallback, observed 2026-08-06T21:50:20.034735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:14.950830Z digest=sha256:7f38ac5fa4d056cb5408f8f47427ca028848dbefecf5cf298cff0aac5467e28c

Observation 72b9e828-054b-4fb2-892e-37b9b0f326ee · outbound

This paper cites Regev, On lattices, learning with errors, random linear codes, and cryptography.

Some Mathematical Problems Behind Lattice-Based Cryptography Regev, On lattices, learning with errors, random linear codes, and cryptography

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:19.847577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:15.175787Z digest=sha256:3199cd4859578a7cc2f12d3a41cebf5c4c4752e5c3232edbf62a68cd8a9146ed

Observation a32188de-8e8e-4df6-88b7-dce1a5b70dd9 · outbound

This paper cites Regev, An Efficient Quantum Factoring Algorithm, J.

Some Mathematical Problems Behind Lattice-Based Cryptography Regev, An Efficient Quantum Factoring Algorithm, J

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:19.643407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:15.282917Z digest=sha256:c40fb0afc9809c9331f914e7c35ebe2e1ff03c91932dcb61abb4337194f64f36

Observation 882eaf8f-028b-4bab-b6e3-ba295eed16d1 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-06T21:50:19.478076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:15.378943Z digest=sha256:eae33989242a306a221dfb9e97d9a26e3eb5f26fa6f4fca89df09769c3e3572d

Observation cd13d1cb-dd92-49d4-95a7-931928ec5d80 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-06T21:50:19.293882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:15.440333Z digest=sha256:03fa3afefb72a13100b37795c24ee52ab4dbec21ce3845d330ccc96bf816e4f3

Observation 048254e6-59ae-4e24-a47d-30b2e4105d06 · outbound

This paper cites Schnorr, A hierarchy of polynomial time lattice basis reduction algorithms.

Some Mathematical Problems Behind Lattice-Based Cryptography Schnorr, A hierarchy of polynomial time lattice basis reduction algorithms

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:19.099505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:15.531166Z digest=sha256:1c205c7de951f9a22dff8114024e7eeafec4ef435a1d13b82baded078db76020

Observation a514e199-9112-4243-9ff0-8a8e946a43c0 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-06T21:50:18.956487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:15.635341Z digest=sha256:bf03baf3aecd7477d2cae6325194d102e44cfe1bc344f071b25139bf5d258934

Observation 42d2c47e-df56-44a5-b57b-fd002ed5ef25 · outbound

This paper cites S¨ odergren, On the distribution of angles between the N shortest vectors in a random lattice,J.

Some Mathematical Problems Behind Lattice-Based Cryptography S¨ odergren, On the distribution of angles between the N shortest vectors in a random lattice,J

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:18.803247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:15.709921Z digest=sha256:9cc4ba5c289b360a50ceba4847d8065bb152c32e42bd8ff8f8915bd54773a7e1

Observation 4b6e40b9-f36f-4ab9-b871-ce0fd95e75f2 · outbound

This paper cites van Emde Boas, Another NP-complete problem and the complexity of computing short vectors in a lattice.

Some Mathematical Problems Behind Lattice-Based Cryptography van Emde Boas, Another NP-complete problem and the complexity of computing short vectors in a lattice

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:18.626018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:15.774177Z digest=sha256:1eaef2688a1cb9336dbb67a1339d25cbe3e520b9e344a6102ef2194e67b6f74d

Observation 30ea6acf-0c5a-4788-8fc4-c571a62cf42e · outbound

This paper cites Viazovska, The sphere packing problem in dimension 8.

Some Mathematical Problems Behind Lattice-Based Cryptography Viazovska, The sphere packing problem in dimension 8

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:18.479360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:15.884297Z digest=sha256:a676a3c16c18678e2316c5afcd0f86abac8f768bfc461500a52cdd3dacd3bf3f

Observation a7bb96ae-764f-4fc2-b104-e5c571383447 · outbound

This paper cites an unresolved cited work.

Some Mathematical Problems Behind Lattice-Based Cryptography Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-06T21:50:18.298685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:15.975734Z digest=sha256:1a518597bd04b8db5f527b2f55debeb7d9bab7caa7c58ea3c5d3d044edf29bf9

Observation 6069ddf7-6a58-4fcc-8f42-40b1f0e278d2 · outbound

This paper cites Zhang and Z.

Some Mathematical Problems Behind Lattice-Based Cryptography Zhang and Z

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:18.169267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:16.092001Z digest=sha256:6155e1c5b0f5c4ffc2c6234d330e6f902d9989186a93760fe309a350927714f9

Observation dd378f69-b89c-4811-8dcc-2d0a16c94456 · outbound

This paper cites Zong, Sphere Packings, Springer-Verlag, New York, 1999.

Some Mathematical Problems Behind Lattice-Based Cryptography Zong, Sphere Packings, Springer-Verlag, New York, 1999

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:17.919103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:16.221291Z digest=sha256:acd50ed877474ca9adb9bdf4911c564be5d40c3379af55c3018d2764bd019e67

Observation 062dc9a4-c2e3-45d0-aa5f-960b1b864315 · outbound

This paper cites Zong, From deep holes to free planes, Bull.

Some Mathematical Problems Behind Lattice-Based Cryptography Zong, From deep holes to free planes, Bull

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:17.601398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:16.392025Z digest=sha256:9fd57f0ca838155f41d0236d5f15a169ac2e9b544ffdfb99f17d262a559431a7

Observation 348212ea-49f6-4dff-8e13-e5c4a698b426 · outbound

This paper cites Zong, Some mathematical mysteries in lattices (Abstract of a plenary talk), ASIACRYPT 2012, LNCS, 7658, 2-3.

Some Mathematical Problems Behind Lattice-Based Cryptography Zong, Some mathematical mysteries in lattices (Abstract of a plenary talk), ASIACRYPT 2012, LNCS, 7658, 2-3

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T21:50:17.403998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:16.528289Z digest=sha256:97200072e4005c99c8d1c93971e32b015df444e24aaf7c535f65a505de2d1627

Observation aa2f4688-2781-4d9a-98c0-90626336a786 · outbound

This paper cites The Mathematical Foundation of Post-Quantum Cryptography.

Some Mathematical Problems Behind Lattice-Based Cryptography The Mathematical Foundation of Post-Quantum Cryptography

Reference 50

Resolution
verified exact
local_arxiv, observed 2026-08-06T21:50:16.897291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-06T21:50:16.650375Z digest=sha256:0334a3ee63fc87bb6e5b761197573d153448de7ec8fa7840a579e418f6d80f0b

Pith citing papers

No inbound Pith citation observations are available.